«Xavier Giné, Robert Townsend, and James Vickery 1 Exposure to drought amongst rural households in India and other countries should, at least in ...»
Statistical Analysis of Rainfall Insurance Payouts in
Xavier Giné, Robert Townsend, and James Vickery 1
Exposure to drought amongst rural households in India and other countries should, at
least in principle, be largely diversifiable. This is because rainfall is exogenous to the
household and not likely to be strongly correlated with the systematic risk factors, such as
aggregate stock returns, that are relevant for a well-diversified representative investor.
With this principle in mind, the goal of rainfall index insurance is to allow households, groups and governments to reduce their exposure to weather risk by purchasing a contract that pays an indemnity during periods of deficient (or excessive) rainfall. Advocates argue that index insurance is transparent, inexpensive to administer, enables quick payouts, and minimizes moral hazard and adverse selection problems associated with other risk-coping mechanisms and insurance programs (see World Bank 2005; Barnett and Mahul 2007; Giné, Townsend, and Vickery 2007).
Dr. Xavier Giné (World Bank, DECRG), Prof. Robert Townsend (University of Chicago), Dr. James Vickery (Federal Reserve Bank of New York). We acknowledge the financial support of the Swiss State Secretariat for Economic Affairs, SECO, CRMG and the Global Association of Risk Professionals, GARP. We thank representatives from ICICI Lombard for their assistance, and Zhenyu Wang for comments. Paola de Baldomero Zazo and Sarita Subramanian provided outstanding research assistance.
Views expressed in this paper are the authors’ and should not be attributed to the World
Bank, Federal Reserve Bank of New York or the Federal Reserve System. Email:
email@example.com, firstname.lastname@example.org, and email@example.com.
This article uses historical rainfall data to estimate the distribution of payouts on a rainfall index insurance product developed by the general insurer ICICI Lombard and offered to rural Indian households since 2003. Our empirical strategy draws on the observation that rainfall in the region we study is close to a stationary process.
Correspondingly we can use historical rainfall data to calculate a putative history of insurance payouts for insurance contracts written against the 2006 monsoon.
We conduct several statistical exercises to better understand the properties of estimated insurance payouts. First, we study the probability distribution of indemnities.
Does the insurance contract pay off regularly, providing income during periods of moderately deficient rainfall? Or does it operate more like disaster insurance, infrequently paying an indemnity, but providing a very high payout during the most extreme rainfall events? Our evidence suggests the truth is closer to the second case.
Analyzing 14 insurance policies, each linked to a different rainfall gauge, we estimate the average probability of receiving a payout on a single phase of insurance coverage is only 11 percent. The maximum indemnity, paid with a probability of around 1 percent, provides a rate of return to the policyholder of 900 percent. We also find that insurance premiums are on average around three times as large as expected payouts.
Second, we study the correlation of payouts in the cross-section and through time.
Spatially correlated rainfall shocks may be more difficult for households to insure against through other means, such as informal risk-sharing arrangements within local kinship groups. This in turn implies larger benefits of a formal rainfall insurance contract. On the other hand, dependence in payouts may also increase the balance sheet exposure of ICICI Lombard or their reinsurers to rainfall risk, by reducing the diversification benefits of holding a pooled portfolio of insurance contracts. Research in corporate finance argues that exposure to risk may reduce firm value when there are informational problems or other frictions in raising external finance (e.g., Froot, Scharfstein, and Stein 1993).
We find no evidence of temporal dependence in payouts. However, it is estimated that rainfall insurance payouts are significantly positively correlated across contracts at a point in time, perhaps unsurprising given that we study policies linked to rainfall within a single geographic region of India. Even so, it is estimated that there are still significant risk-reduction benefits from holding a diversified portfolio of contracts. The standard deviation of payouts on an equally-weighted basket of 11 different insurance policies is only half as large as the standard deviation of an average individual contract.
Third, we find some evidence that insurance payouts are negatively correlated with growth in Indian per capita GDP. This suggests that some component of rainfall risk is aggregate to the Indian economy as a whole, perhaps reflecting the size and importance of the Indian agricultural sector for employment and economic activity.
Background and Methodology We study a rainfall insurance product developed by the general insurer ICICI Lombard, which has been offered to rural Indian households since 2003. ICICI Lombard partners with local financial institutions to market the insurance to households. Giné, Townsend, and Vickery (2007) and Cole and Tufano (2007) provide detailed background about the insurance product. Giné, Townsend, and Vickery (2007) also study the determinants of household insurance purchase decisions, based on a 2004 household survey.
Our analysis focuses on calendar year 2006 insurance contracts linked to rainfall in the southern Indian state of Andhra Pradesh. Below, we briefly summarize the design of these contracts. Policies cover rainfall during the Kharif (monsoon season), which is the prime cropping season running from approximately June to September. The contract divides the Kharif into three phases roughly corresponding to sowing, podding/flowering and harvest. The first two phases are 35 days in duration, while the third (harvest) phase is 40 days long. In 2006, farmers were allowed to purchase different numbers of contracts across each of the three phases.
Phase payouts are based on accumulated rainfall between the start and end dates of the phase, measured at a nearby reference weather station or rain gauge.1 The start of the first phase is triggered by the monsoon rains. Namely, phase 1 (sowing) begins on the first date on which accumulated rain since June 1 exceeds 50mm, or on July 1 if accumulated rain since June 1 is below 50mm.
Insurance payouts in the first two phases are linked to low rainfall. The payout structure in these cases is illustrated in figure 1. Contract details in the figure are from the phase 1 contract linked to the Mahabubnagar weather station, which is representative of the policies studied in our empirical analysis. The policy pays zero if accumulated rainfall during the phase exceeds an upper threshold, or ‘strike’, which in this case is 70mm.
Otherwise, the policy pays Rs. 10 for each mm of rainfall deficiency relative to the strike, until the lower threshold, or ‘exit’, is reached. If rainfall is below the exit value, the policy pays a fixed, higher indemnity of Rs. 1000. Phase 3 policies have the same structure, but in reverse, they pay out only when rainfall exceeds the strike, meant to correspond to unusually heavy rainfall during the harvest that causes damage to crops.
Depending on the policy, the reference weather station is one of three types: an Indian Meteorological Department (IMD) station, mandal rainfall station (a mandal is a local geographic area roughly equivalent to a U.S. county) or one of a network of automated rain gauges installed by ICICI Lombard. For this article, we focus on IMD rainfall data. These are considered to be more reliable than data from mandal stations, and include a longer and more complete history of past rainfall to construct a putative dataset of insurance payouts.
Our source data consist of policy terms for contracts indexed to 14 different IMD weather stations in Andhra Pradesh (one contract per station), as well as IMD historical rainfall data for each station. Rainfall data are measured at a daily frequency. Although the earliest rainfall data is from 1970, the starting point of the data varies by weather station, and there are also scattered individual months and years where data is missing.
Across 14 stations, there are 1,089 individual contract phases for which at least some rainfall data is available. However, for 135 phases data is missing for at least one day during the contract period. We drop these from our analysis, leaving a sample of 954 phases for which we have complete daily rainfall to calculate payouts.
The amount of missing data varies significantly across weather stations. At one extreme there are 91 phases of complete rainfall data for the Anantapur weather station (equivalent to 30.3 monsoon years). At the other extreme, for the Adilabad and Nalgonda stations, only a small number of complete phases of rainfall data is available (8 and 18 phases respectively). At least 64 phases (21.3 monsoon years) of complete daily historical data is available for 11 of the 14 stations; our empirical findings are similar if we restrict analysis to these stations only.
Applying the insurance contract terms to historical rainfall data, we calculate the hypothetical payout on the contract for each station, phase and year. Data on estimated payouts and information on contract features are presented in table 1. Strikingly, the insurance pays an indemnity in only 10.7 percent of phases, a point we return to below.
The average estimated payout is Rs. 29.7, compared to an average premium of Rs. 99.9.
This wedge presumably reflects, at least in part, the administrative and financing costs of designing, underwriting and selling insurance policies, especially given the small current size of the market and lack of associated economies of scale. Although the insurance is not actuarially fair, it may still be valuable to policyholders if it pays an indemnity in times when the household’s marginal utility of consumption is particularly high.
Distribution of payouts Evidence on the distribution of payouts is presented in figure 2. The x-axis for the graph is ‘payout rank,’ which ranks payouts in increasing order of size, expressed on a scale from 0 to 1. Figure 2 plots payout amount against payout rank. The payout is zero up to the 89th percentile, indicating that an indemnity is paid in only 11 percent of phases. The 95th percentile of payouts is around Rs. 200, double the average premium. In a small fraction of cases (around 1 percent), the insurance pays the maximum indemnity of Rs.
1000, yielding an average return on the premium paid of 900 percent.
Figure 2 suggests that the ICICI Lombard policies we study primarily insure farmers against extreme tail events of the rainfall distribution. Confirming this graphical evidence, we calculate that around one-half of the value of indemnities is generated by the highest-paying 2 percent of phases. Without further evidence on the sensitivity of household consumption to rainfall shocks of different types, it is difficult to say whether this structure approximates the optimal insurance design. For example, Paxson (1992) and Jacoby and Skoufias (1998) are generally unable to reject that consumption of rural households in Thailand and India respectively is fully insured against rainfall fluctuations. However, these two papers do not consider whether the degree of consumption insurance is lower for extreme shocks, such as a severe drought, which could for example exhaust the household’s stock of precautionary savings.
From the perspective of ICICI Lombard, the skewed distribution of payouts suggests a significant reserve of liquid funds may need to be held against policies whose risk is not transferred to reinsurers. This in turn could be costly due to informational frictions in raising external finance or tax disadvantages in holding capital (Zanjani 2002;
Froot 1999; Froot and Stein 1998). Amongst other factors, the insurer’s exposure to risk will depend on the value of policies originated, the extent to which reinsurance is used, and correlation of insurance payouts across contracts and through time. We present some evidence on these correlations in the next section.
Dependence in insurance payouts To calculate the degree of cross-sectional dependence in payouts, we calculate the standard deviation of phase payouts for each weather station, restricting analysis to the 11 contracts for which we have the most historical rainfall data. The average of these 11 estimated contract standard deviations is Rs. 112.3. We then calculate the standard deviation of the mean insurance payout averaged across the 11 stations at each point in time. This standard deviation will in general be smaller than 112.3, reflecting the diversification benefits from pooling a portfolio of contracts whose returns are not perfectly correlated. If insurance payouts are independent, the standard deviation of the mean payout will asymptotically be 1/ 11 times as large as the standard deviation of individual contract payouts (i.e.1/ 11 × 112.3 = Rs. 33.9, a reduction in the standard deviation of 70%). In contrast, if payouts are perfectly correlated across contracts, there would be no difference between the standard deviation of the mean payout and those of the individual contracts.
Empirically, we calculate that the standard deviation of the mean payout is Rs.
60.7, 46% smaller than the average standard deviation of individual contract payouts.
This reduction in the standard deviation is smaller than 70%, indicating that insurance payouts are positively correlated cross-sectionally. However, there are still surprisingly large diversification benefits from holding a portfolio of insurance contracts, even though all insurance payouts are driven by rainfall in the same Indian state. Diversification would be larger still if contracts are pooled over a wider geographic area.